# Tagged Questions

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### The “dynamics” of foliations

My mathematical interests revolve mainly around dynamical systems, and (unfortunately) I don't have as much general culture in geometry as I would like (and I should...) I often see foliations come ...
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### A proof of a theorem of Liouville

I need some reference for the proof of the following theorem attributed to Liouville: Theorem: Let $f(x):\Omega\longrightarrow \mathbb R^n$ a $C^2$ function where $\Omega$ is an open subset of ...
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### Tool for generating mathematical billiards

i'm currently looking for some program which can generate arbitrary mathematical billiards and trajectories inside them. Any help would be much appreciated! Thanks/ Mats
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### expansive toral automorphism and forward expansive toral endomorphism

I've been trying to find in the literature a rigorous formal proof for the next two equivalences: $d$-dimensional toral automorphisms are expansive iff they are hyperbolic. $d$-dimensional toral ...
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### Reference book for “Dynamical Systems”

I want to do my thesis about oscillations. I am a math student so I enjoy rigorous texts and hate sketchy ones. I am looking for a textbook or a good source that could help me with dynamical systems. ...
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### Best book for Three-Body Problem

Can anybody advise me the most essential reference for the three-body problem? I need a book with the problem in different system of coordinates and how actually this changes are performed (synodic, ...
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### A Category Theoretical view of the Kalman Filter

Some basic background The Kalman filter is a (linear) state estimation algorithm that presumes that there is some sort of uncertainty (optimally Gaussian) in the state observations of the dynamical ...
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### Reference request for differential geometry/quantum chaos text

I'm looking for a differential-geometry based exposition of chaos theory and quantum chaos. Ideally, it would start with the Hamiltonian formalism (on symplectic manifolds) and discuss as many of the ...
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### Explicit form of strange attractors

Are there any examples of continuous-time dynamical systems possessing strange attractors for which there exist explicit formulas describing these attractors? Many thanks in advance and apologies if ...
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### Difference between dynamic system and complex system

I know this might not be an easy question, I've already read the wikipedia page, and there is an interesting view: Therefore, the main difference between chaotic systems and complex systems is ...
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### Ideas about an Ordinary Differential Equations research work (University level)

Good afternoon to everyone, I need some ideas about a Ordinary Differential Equations research work. It is for the ODE subject that I am doing at my Mathematics degree in my University. They asked me ...
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### transversal homoclinic points on a higher-dimensional torus

In many sources (for example introduction to chaotic dynamical systems by Devaney) one can find a proof of the fact that the transversal homoclinic points (points which lay on both stable and unstable ...
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### Lyapunov exponent reference

I know a little bit of probability; but I do not know anything from dynamical systems. I want to understand the notion of Lyapunov exponent for a certain sequence of random variables arising out of a ...